I have seen that Euclid's Elements was written 300 BC and first set in type in 1482. Are there scans of that old versions available?

How were formulas / images added to the books created with printing presses? Can / could formulas / images also be printed automatically or had they to draw every single image again for every single new book?


  • $\begingroup$ Interesting answers. I also find the symbology of the frontispiece from the Tabulae Rudolphinae (1627) by Kepler and that of Opere (1761) by Jacopo Riccati fascinating. Any others? $\endgroup$ Jan 25, 2022 at 16:03

3 Answers 3


Euclid's Elements of Geometry (1482)

In the 1455 Gutenberg bible the illustrations were hand-drawn after printing.The illustrations in the 1482 Elements were printed. [In some copies the diagrams were colored in by hand, see right image above.]

In a foreword the printer Erhard Ratdolt attributed the prior lack of printed mathematical works to the difficulty produced by the diagrams, and adds "Having perceived, that it was this alone that formed an obstacle to something that would be useful to all, I have achieved, by applying myself to the problem and not without putting in much hard work, that geometrical figures can be composed with the same ease as movable type".

There appears to be some uncertainty on the nature of Ratdolt's method, which he did not explain any further. The common practice in the 15th century was to use woodcuts for illustrations, as discussed by Bowers. Alternatively, according to this source, Ratdolt had devised elementary geometrical forms in type metal which could be combined to form figures which, being in metal, could be printed at the same time as the typeset page.

The OP asks also for early printed formulas. The earliest appearance of + and - symbols appears to be Johannes Widmann (1489), see image below. Notation that would need subscript or superscripts (such as exponents) was generally avoided, as were fractions with a bar. A quote: The bar is generally found in Latin manuscripts of the late Middle Ages, but when printing was introduced it was frequently omitted, doubtless owing to typographical difficulties. This inference is confirmed by such books as Rudolff's Kunstliche rechnung (1526), where the bar is omitted in all ordinary fractions but is inserted in fractions printed in larger type and those having large numbers.

  • $\begingroup$ That looks awesome! $\endgroup$ Aug 11, 2014 at 19:34
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    $\begingroup$ Although I see some images, I can't find any formula. Didn't they use fractions / systems of equations / exponentiation / roots at that time? If they used it: Was that also made with woodcut? Isn't woodcut too weak to be used with printing presses? $\endgroup$ Aug 11, 2014 at 20:32
  • $\begingroup$ @moose --- the link to Bowers' article that I added explains that wood blocks were preferred for illustrations over metal plates because they can take more wear before becoming unusable. Still, Ratdolt's comment suggests he used specially designed metal type for the drawings as well as for the text. $\endgroup$ Aug 11, 2014 at 21:56
  • $\begingroup$ @moose --- I also added some info on early use of formulas $\endgroup$ Aug 12, 2014 at 8:53
  • $\begingroup$ Those pages from Euclid are beautiful, but I would hate to have had to learn my geometry from them! $\endgroup$ Jan 25, 2022 at 22:33

The following references describe mathematical printing in the 1950s, before it became too expensive and degenerated into illegible typescript:

The Printing of Mathematics by T. W. Chaundy, P. R. Barrett and Charles Batey, Oxford University Press, 1954.

Setting Mathematics by Arthur Phillips, in The Monotype Recorder 40 (4), Winter 1956.

Printing Mathematics by Peter Basnett, in Eureka 23 (1960) 11-13.

The Mathematician and the Printer. Hints on the preparation of mathematical and technical manuscripts. by R. G. Hitchings, Hodgson, London, 1961.

Copy-Editing, The Cambridge Handbook for Editors, Authors, Publishers, by Judith Butcher, CUP. First edition 1975, second 1981, third 1992.

At that time, ordinary text (novels and newspapers) was set using the Linotype system, in which the compositor would use a huge keyboard to select characters and then they would be set in molten lead a whole line at a time.

However, this was unsuitable for mathematics and the "state of the art" was the Monotype Four Line System, which had movable type. The following piece of nonsense is a block provided by Monotype and used in the Eureka article:

enter image description here

Each letter is set on a block (shown in grey) that occupies space on one of the four lines. However, the $g$, $X$, $b$ and $Y$ overhang their blocks and are supported by spacer blocks (white) in the other line.

You could add big integral or summation signs in front of such a fractional expression, and (I think) a $d x$ vertically centered after it.

PS on OCR (Optical Character Recognition)

There is commercial software for OCR of maths but apparently no good FOSS. For ordinary text, Tesseract-OCR does a very good job, but its "equation" recognition seems to be limited. This article by Ray Smith of Google gives a good description of how it works.

There are comments on the Web asking for recognition of general LaTeX output or handwritten mathematics. These are fanciful because they are over-ambitious, not clearly defined and not what is actually required.

On the other hand there are huge numbers of old journal papers (increasingly available online as scans) that were printed with the technology described above, or less. It would be extremely valuable to be able to put these in digital form, for example for machine translation.

Anyone interested in a programming project (maybe contributing to tesseract) should therefore aim to recognise the Monotype "four line" formulae above. Of course it would also be necessary to recognise symbols, fonts, sub- and superscripts. All of these would appear to be within the design concept of tesseract.

Such a project should be regarded as a tool to help a human digitise the text, ie to reduce the amount of hand-editing that is needed but not necessarily eliminate it.

This post should be enough on its own to start such a project. More details of the old printing technologies are in the books and articles mention at the top of this post. I have copies of these that were kindly given to me (a long time ago) by David Tranah of CUP.

  • $\begingroup$ I tried to fix the LaTeX, but I'm not sure this is what you intended; if I just enter your text into a LaTeX processor it complains with "Ambiguous; you need another { and }". $\endgroup$ Aug 17, 2014 at 10:26
  • $\begingroup$ LaTeX --> image, for clarity. $\endgroup$ Aug 17, 2014 at 12:13

Printing requires pressing the mould against a hard surface with only a paper in between. This damages wood carvings, so they have a limited number of prints. In modern times, Escher, for example, used a Japanese technique that involved pressing the prints with bones. This was nicer to the engraving, but very time consuming and not so suitable for line production.

In later times, the chemistry allowed engraving metal, the etching. A sheet of copper is covered in a varnish, and the drawings are done removing selectively this layer. When finished, the sheet is submerged in acid, that corrodes the exposed metal, but leaves the areas protected by varnish.


As adding any non text to printed books was so difficult, mathematical notation developed slowly. For example, the equal sign was not invented until 1557. Before that, they just spelled it out (or used Latin abbreviations). More advanced symbols, requiring reordering the elements of the text (the equal sign is just one character more in text), may have been invented before, but it would take a lot of effort to communicate to the rest of mathematicians.

  • $\begingroup$ How do you know that it was 1557? $\endgroup$ Aug 11, 2014 at 21:58
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    $\begingroup$ @moose enciclopedic memory, id est, I remembered to look it up in Wikipedia. (I forgot to add the link). $\endgroup$
    – Davidmh
    Aug 11, 2014 at 22:01

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